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Molecular Cooperation to Reinforce Immune
Response during Carcinoma: a Structural
Bioinformatics Analysis
R. PIZZI1, T. RU...
Scaletta:
1. Evidences:
-immune-neuroendocrine relationship
-a neuroendocrine substance:Melatonin
-melatonin has anti-canc...
-immune-neuroendocrine relationship
-a neuroendicrine substance:Melatonin
-melatonin has anti-cancer effect (sinergy,
Liss...
Melatonin is a biogenic amine that is found in animals, plants and
microbes. Aaron B. Lerner of Yale University is credite...
IL-2
LPS
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 2014
OUR hypothesis
-biological frame: actors
-simulation methods
-molecular recognition(interactions,
complementarities)
-docking tools
-HEX ...
• Simulation tools
• Why we chose HEX
HEX Dave Ritchie-
Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France
• Hex is an interactiv...
Due to the special orthogonality property of the basis functions, the correlation (or overlap as
a function of translation...
Closely related to the protein docking problem is the molecular similarity problem - i.e. how to
find the relative orienta...
Rotational Search
Generally, the docking search proceeds by rotating the receptor and ligand about their centroids at each...
The calculation is arranged so that the intermolecular twist angle search is in the innermost loop of the search. The sear...
HEX Dave Ritchie-
Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France
Docking examples
This ...
5.6 Molecular Mechanics Refinement
In addition to the bumps counter, a single (rigid body) molecular mechanics energy may ...
5.7 Clustering Docking Results
The default docking search range and clustering parameters are normally sufficient to gener...
5.12 Molecular Matching
Hex superposes or matches pairs of molecular structures using the same 3D density representation a...
-steps description and importance
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 20...
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 2014
4.Results
-IL_2: fig1(sinix), f...
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 2014
4.Results
-MLT: fig5,2,6,4 (in ...
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 2014
4.Results
-LPS: fig 7,3,6,4 (in...
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 2014
8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING.
Florence, 2014
5. Conclusions
-internal controls
-this preliminary study has allowed to observe that the
simultaneous presence of Melaton...
Molecular cooperation to reinforce immune response during carcinoma (1)
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Molecular cooperation to reinforce immune response during carcinoma (1)

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A structural bioinformatics study on the interaction between immune cells, melatonin and other molecular structures on a neoplastic tissue.

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Molecular cooperation to reinforce immune response during carcinoma (1)

  1. 1. Molecular Cooperation to Reinforce Immune Response during Carcinoma: a Structural Bioinformatics Analysis R. PIZZI1, T. RUTIGLIANO1, P. GUADALUPI2 and M. PREGNOLATO3 1Computer Science Department,University of Milan 2 Central Maine Medical Center, USA 3Department of Drug Sciences, University of Pavia
  2. 2. Scaletta: 1. Evidences: -immune-neuroendocrine relationship -a neuroendocrine substance:Melatonin -melatonin has anti-cancer effect (sinergy, Lissoni) 2. our hypothesis (sinergy between..) 3. material and methods -biological frame: adenocarcinoma, lipid bilayer (image), actors (ligands and receptors) -simulation methods -in generale: molecular recognition(interactions, complementarities) -docking tools -HEX (rigid box, energy minimization, SPF . Formula included)(perchè lo abbiamo scelto) -experimental design: steps di docking 4.Results - IL2: fig 1,2 - MLT: fig 5,2,6,4 (organized in 1slide) - LPS: fig 7,3,6,4 (organized in 1slide) 5. Conclusion -internal control -this preliminary study has allowed to observe that the simultaneous presence of Melatonin, IL-2 and LPS resulted in changes in the behavior of ligands compared to position inside the natural receptors occupied in the absence of other ligands - It can therefore be concluded that as hypothesized, namely the existence of an interaction between neuroendocrine agents, immune substances and mediators of the inflammatory and / or antitumor response as LPS, has an effective confirmation at the level of computational simulation
  3. 3. -immune-neuroendocrine relationship -a neuroendicrine substance:Melatonin -melatonin has anti-cancer effect (sinergy, Lissoni) 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 1.Evidences:
  4. 4. Melatonin is a biogenic amine that is found in animals, plants and microbes. Aaron B. Lerner of Yale University is credited for naming the hormone and for defining its chemical structure in 1958. In mammals, melatonin is produced by the pineal gland. The pineal gland is small endocrine gland, about the size of a rice grain and shaped like a pine cone (hence the name), that is located in the center of the brain (rostro-dorsal to the superior colliculus) but outside the blood-brain barrier. The secretion of melatonin increases in darkness and decreases during exposure to light, thereby regulating the circadian rhythms of several biological functions, including the sleep-wake cycle. In particular, melatonin regulates the sleep-wake cycle by chemically causing drowsiness and lowering the body temperature. Melatonin is also implicated in the regulation of mood, learning and memory, immune activity, dreaming, fertility and reproduction. Melatonin is also an effective antioxidant. Most of the actions of melatonin are mediated through the binding and activation of melatonin receptors. Individuals with autism spectrum disorders (ASD) may have lower than normal levels of melatonin. A 2008 study found that unaffected parents of individuals with ASD also have lower melatonin levels, and that the deficits were associated with low activity of the ASMT gene, which encodes the last enzyme of melatonin synthesis. Reduced melatonin production has also been proposed as a likely factor in the significantly higher cancer rates in night workers.
  5. 5. IL-2
  6. 6. LPS
  7. 7. 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 OUR hypothesis
  8. 8. -biological frame: actors -simulation methods -molecular recognition(interactions, complementarities) -docking tools -HEX (rigid box, energy minimization, SPF . Formula included) -experimental design (adenocarcinoma, membrane, docking of receptors and ligands) 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 3. material and methods
  9. 9. • Simulation tools • Why we chose HEX
  10. 10. HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France • Hex is an interactive molecular graphics program for calculating and displaying feasible docking modes of pairs of protein and DNA molecules. Hex can also calculate protein-ligand docking, assuming the ligand is rigid, and it can superpose pairs of molecules using only knowledge of their 3D shapes.Hex has been available for about 12 years now, but as far as I know, it is still the only docking and superpostion program to usespherical polar Fourier (SPF) correlations to accelerate the calculations, and its still one of the few docking programs which has built-in graphics to view the results. Also, as far as I know, it is the first protein docking program to be able to use modern graphics processor units (GPUs) to accelerate the calculations. • In Hex’s docking calculations, each molecule is modelled using 3D expansions of real orthogonal spherical polar basis functions to encode both surface shape and electrostatic charge and potential distributions. Essentially, this allows each property to be represented by a vector of coefficients (which are the components of the basis functions).Hex represents the surface shapes of proteins using a two-term surface skin plus van der Waals steric density model, whereas the electrostatic model is derived from classical electrostatic theory. By writing expressions for the overlap of pairs of parametric functions, one can obtain an overall docking score as a function of the six degrees of freedom in a rigid body docking search. With suitable scaling factors, this docking score can be interpreted as an interaction energy, which we seek to minimise
  11. 11. Due to the special orthogonality property of the basis functions, the correlation (or overlap as a function of translation/rotation operations) between a pair of 3D functions can be calculated using expressions which involve only the original expansion coefficients. In many respects, this approach is similar to conventional fast Fourier transform (FFT) docking methods which use Cartesian grid representations of protein shape and other properties, and which then use translational FFTs to perform the docking correlations. However, the Cartesian grid approach only accelerates a docking search in three translational degrees of freedom whereas the SPF approach allows the effect of rotations and translations to be calculated directly from the original expansion coefficients. Even though the FFT part of a docking search may be fast, the overall speed of calculation still depends very much on the initial "set-up" costs and the final "post-processing costs" of filtering and perhaps clustering the results. Hex is fast because it uses FFT correlations as much as possible, and because the "set-up" costs are much lower in the SPF approach than in Cartesian grid-based approaches. It also turns out that the FFT part of the calculation maps very well to the GPU hardware. Thus, further speed-ups can be expected if you have a suitable graphics card. Although it is not always easy to compare the performance of different docking algorithms because a lot depends on the size of the translational or rotation steps used, for example, I would still claim that Hex is at least 10 times faster than conventional FFT docking algorithms. Hex is also very easy to use. However, to use Hex most effectively, it can sometimes require some thought when setting up the calculation, especially when setting up the starting orientations of the proteins to be docked. In the spherical polar approach, it is natural to assign the six rigid body degrees of freedom as five Euler rotation angles and an intermolecular separation. Thus, in complete contrast to Cartesian based FFT approaches, the rotational part of a docking search is the “easy bit” and modelling translations becomes the “hard part.” Fortunately, however, only a few translations (typically about 40 steps of 0.75 Ångstrom) are required to complete a six dimensional docking search. One advantage of the spherical polar approach is that it is easy to constrain the docking search to one or both binding sites, when this knowledge is available, simply by constraining one or two of the angular degrees of freedom. This can reduce docking times to a matter of minutes on a modern workstation. HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France
  12. 12. Closely related to the protein docking problem is the molecular similarity problem - i.e. how to find the relative orientation of a pair of similar molecules such that some measure of the similarity (difference) between the molecules is maximised (minimised). Both problems involve translating and rotating one or both molecules into the desired orientation. However, to a first approximation, the similarity problem can be reduced to a three dimensional rotational search by initially placing both molecules in a common coordinate system. Although Hex will remain primarily a docking program, the 3D superposition calculations implemented in Hex demonstrate the potential for performing fast 3D superpositions using the SPF correlation approach. Work is in progress to develop this approach further as a separate program for high throughput ligand screening. (When using a complex structure, you should ensure that the chain names and residue numbers are consistent with those of the receptor and ligandbecause Hex uses this information to identify and hence superpose corresponding pairs of alpha-carbon atoms from each chain in order to calculate RMS deviations between the docked position of the ligand and its position in the known complex) HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France
  13. 13. Rotational Search Generally, the docking search proceeds by rotating the receptor and ligand about their centroids at each of a range of intermolecular distances. The receptor and ligand are each assigned two Euler rotation angles, and the final rotation is defined as a twist of the ligand about the intermolecular axis. The default behaviour is then to perform a full six-dimensional search over the full rotational ranges. However, more limited docking searches can be performed in which the allowed angular and distance ranges may be constrained by the user. The docking coordinate system is illustrated in Figure 6 below Figure 6. Illustration of spherical polar docking with respect to the intermolecular axis. An initial docking orientation may be defined by specifying which residues should be located at the local coordinate origin for each molecule, and by defining "interface residues" which will be located on thez-axis. The docking search may be restricted by defining a “range angle” for the receptor and/or ligand orientations. If range angles are defined, then the interface residues will always be constrained to appear within a spherical cone defined by the corresponding range angle. This illustration shows two range angles, each of 45 degrees. HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, Fran
  14. 14. The calculation is arranged so that the intermolecular twist angle search is in the innermost loop of the search. The search around the twist angle may be accelerated using a 1D FFT. Alternatively, all three Euler angles assigned to the ligand can be searched together using a 3D FFT. In the Linux version, all five rotation angles may be searched together using a 5D FFT. However, this requires at least 1 gigabyte of memory to hold the very large 5D rotational grid. Note. The speed of the 3D and 5D FFT calculations depends very much on the quality of FFT code, and whether it exploits any hardware acceleration. For CPU-based docking, the Intel MKL code is about twice as fast as FFTW, which is about one and a half times as fast my own multi-dimensional FFT code which is partly based on Kiss FFT, and which doesn’t use any assembly or SSE instructions. However, only the Linux version of the MKL library is available for free to non-profit organisations. So docking is fastest with the Linux version ofHex. I do not use the FFTW code because I do not agree with its GPL license conditions. Hence, 3D and 5D docking correlations on the Windows and Mac versions of Hex is relatively slow. For GPU-based docking, 1D correlations using cuFFT, on a high-end GeForce or Quadro card are much faster than on a high-end CPU. Compared to using a single high-end CPU (3.2GHz i7-965), the same calculation on a high-end GPU (FX-5800) is about 45x faster (Ritchie and Venkatraman, manuscript in preparation). DEFAUL PARAMETERS: There are several controls which specify the resolution, and in particular the order, N, of the docking correlation. The default settings are for the program to perform an initial Steric Scanat N=16, followed by a Final Search at N=25, using just the steric contribution to the docking energy. In this mode, about all but the top 30,000 orientations are discarded after the Steric Scan. The Steric Scan may be toggled off, in which case every orientation is evaluated using a steric correlation (and optionally an electrostatic correlation) to order N, as given the Final Search slider. Although the default is to use correlations to N=25, in Rounds 3–5 of the CAPRI blind trial, I found that better results are obtained using N=30 correlations (see section References). Generally, N=30 is recommended when docking high resolution crystal structures for which the conformational change on binding is expected to be small. N=25 should be used when docking model-built structures or structures which are expected to be more flexible. As rule of thumb, I would use N=16 for the scan stage with final scoring at N=30, and I would use scans using N=20 when scoring with N=30. In some cases, a good solution can be missed with the N=16 scan. It is safer, but obviously slower always to use N=20 for the initial scan. Distance Sub-Stepping Hex performs the high resolution Final Searchcorrelation using smaller distance incerements than are used for the fast low resolution Steric Scan phase. This allows the search space to be covered more rapidly (coarsely) in the first phase, but more finely in the final phase. This behaviour is controlled by theDistance Range, Scan Step and SubSteps parameters in the Docking Control panel. The default values areDistance Range=40, Scan Step=0.75, SubSteps=2. This means that the Steric Scan phase will search over 55 distance increments of +/- 0.75 Å from the starting separation, plus the starting separation itself). These orientations are sorted by calculated energy, and a new set of trial orientations are generated for the top-scoring 10,000–20,000 orientations using the Scan Step andSubSteps parameters to construct new distance samples in steps of +/-(Scan Step)/(Substeps) from the initial orientations. In other words the default behaviour is essentially to scan the search space at 1Å resolution, but to perform the high resolution scoring at 0.5Å resolution. Setting SubSteps=0 gives the old behaviour of earlier versions in which a constant distance step is used for both resolution levels. HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France
  15. 15. HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France Docking examples This says that the Steric Scan (N=16) phase of the docking calculation will be performed at (1+40)/0.75=53 intermolecular separations, in +/- steps of 0.75 Å starting from the current distance posted in the R slider in the bottom border of the main window. The Final Search (N=25) phase will be applied to the the highest scoring scan orientations in steps of 0.75/2 Å, as described above. The rotational search will use angular increments of about 7.5 degrees in each of the two ligand and receptor rotational angles, and in steps of 5.5 degrees about the twist angle. Internally, the given step sizes will be adjusted to give computationally convenient numbers of samples. For example, a step size of 5.5 degrees will actually give 64 samples (360/64=5.625). Specifying a step size of 7.5 degrees will give 48 or 24 angular samples in the corresponding FFT grid, or it will select an icosahedral tesselation with 812 vertices because that is the tesselation order which will give an average angular distance between neighbouring pairs of vertices of about 7.5 degrees. A Cartesian grid is used to sample the molecular skins numerically but this grid plays no further role in the calculation once the surface skin expansion coefficients have been determined. Most conventional FFT docking algorithms have to use rather large grids (e.g. 1 Ångstrom cubes) because the grid must accommodate all possible translations of the ligand about a stationary receptor. Here, the grid only needs to contain the larger of the two molecules so that much finer sampling grids are feasible. In Hex, a 0.6 Ångstrom grid seems to work well and is still reasonably fast to calculate. The sampling grid size may be varied using the Grid Dimension selection box. The calculation of the surface skins used in the docking correlation is controlled by the parameters in the Surface Control panel. The default values do not normally need to be changed. It should be noted that such docking calculations never give a unique solution. Rather, Hex sorts the generated orientations by docking energy and prints a summary of the 10,000 highest scoring (lowest energy) orientations. The best 500 orientations are retained for viewing.
  16. 16. 5.6 Molecular Mechanics Refinement In addition to the bumps counter, a single (rigid body) molecular mechanics energy may be calculated for each docking solution (MM Energies), or a Newton-like energy miminisation (MM Minimisation) can be applied to each docking solution. These energies are calculated using “soft” Lennard-Jones and hydrogen bond potentials, adapted from the OPLS force-field parameters, along with an explicit charge-charge electrostatic contribution. When docking complexes where conformational changes are known to be small, this gives an effective way to prune many “false- positive”orientations and to enhance the energy of the “right answer”. However, this rigid-body refinement procedure should not be used if conformational changes are expected to be large because (despite using soft potentials) it tends to eject ligands with incorrect conformations from the binding site. This part of the program is still “under development”. 5.7 Clustering Docking Results Because Hex uses essentially a brute-force search approach to the docking problem, it is advisable to over-sample the search space rather than to risk missing a good solution by under-sampling the space. However, this can cause multiple similar but incorrect orientations (false-positives) to push good solutions down the list. By default, Hex uses a simple clustering algorithm to group spatially similar docking orientations. Each docking solution is first ordered by energy, and the lowest energy solution is made the seed orientation for the first cluster. The list is then searched down to a given depth for other similar orientations whose main-chain alpha-Carbon RMS deviation is within a given threshold (default 3Å RMS) of the seed orientation, and these orientations are then assigned to the first cluster. The process is then repeated starting from the next lowest unassigned orientation, until all solutions have been assigned to a cluster. The Cluster Window parameter may be used to control the search depth when looking for cluster members. Because clustering uses a simple but inefficient algorithm (rather like a “bubble-sort”), it is advisable use this parameter to limit the search depth if the number of saved solutions is large. HEX Dave Ritchie- Team Orpailleur, INRIA Nancy Grand Est, LORIA, 54506 Vavdoeuvre-les-Nancy, France
  17. 17. 5.7 Clustering Docking Results The default docking search range and clustering parameters are normally sufficient to generate good coverage of the search space, and to distinguish different but similar solutions. But you may wish to experiment. Clustering is re- calculated whenever a clustering parameter is changed, without having to re-run the docking search. Here, “good coverage”means that for each docking orientation, there is about a 99% chance of generating at least one other solution within 3Å RMS of the first one (unpublished experiments). Deciding whether or not two similar but different orientations ought to fall within the same cluster is somewhat subjective. The 3Å threshold seems to work well for large-ish ligands (roughly 100 residues), but should probably be reduced for smaller ligands. In the CAPRI blind docking experiment, I tend to use a large threshold of, say, 5Å to try to improve the chances of finding at least one “medium accuracy” prediction within the first 10 predictions submitted). But this doesn’t always help! 5.10 Docking Very Large Molecules (Macro Docking) The radial shape functions used in Hex decay exponentially beyond about 35 Ångstroms from the chosen origin. This means that the shapes of proteins much larger than this are not represented well. One example of such a large protein is the viral-surface hemagglutinin molecule presented in the CASP II and CAPRI protein docking challenges. In order to dock such large molecules,Hex assigns multiple local coordinate systems to the larger molecule (assumed to be the receptor) and docks the ligand around each local coordinate frame on the receptor. Setting up the receptor coordinate systems is controlled by theControls ... Macro-Sampling control panel. The general approach is to construct a very low resolution spherical harmonic surface representation of the receptor (say, setting L=5 in the Harmonics Control panel), and then to cover this surface with a large number of spheres. These spheres are placed using the surface normals of each triangular patch used to draw the harmonic surface. The spheres are then iteratively culled, where the sphere with the greatest overlap with its neighbours is culled at each iteration. This is repeated until some pre-set number of spheres (default 25) remain - these should still cover the surface, but be reasonably well-dispersed. The positions of these spheres are then used to generate initial docking orientations for the ligand over the receptor, and an appropriate local coordinate frame is derived from the geometry. For multi-domain receptors, each sphere can be assigned to a source chain, and spheres that do not belong to a given chain may optionally be excluded. The gives a simple (but imperfect) way to limit the docking search to one of several symmetry-related domains (as in the hemagglutinin case, for example). In order to set up such a calculation for an antibody/antigen system (where the antibody’s binding site is known), it is a good idea to orient the ligand (antibody) such that the binding site faces the receptor - i.e. the principal intermolecular axis passes near the antibody hypervariable loops. This can be achieved by manually editing the antibody into position. Then, the macro-sampling algorithm will place the ligand (antibody) at each of the generated starting orientations and in each orientation the antibody will be transformed to face the receptor. Using the main Docking Control panel, a search range of 45 degrees should be set for both the ligand and receptor so that the docking search will gyrate each molecule about the local intermolecular coordinate system yet still keep each molecule roughly facing the other as defined by the starting pose.
  18. 18. 5.12 Molecular Matching Hex superposes or matches pairs of molecular structures using the same 3D density representation as for docking. Superposition is very much like docking, except now the search is for maximum similarity rather than maximum complementarity. Superposition calculations can only be performed once you have opened a receptor and a ligand molecule. If you want to superpose a pair of molecules that originate from the same PDB file, you will have to manually edit the molecules into separate PDB-format files. Superposition calculations are controlled by the parameters in theMatching Control panel. To calculate a superposition using the default settings (which are usually reasonable), use: Controls ... Matching ... Activate Hex will take a few seconds to calculate the steric density functions for each molecule. It will then systematically search over the range of angular and intermolecular distance samples given in theMatching Control panel. However, unlike docking, Hex first translates the ligand’s centre of mass to coincide with that of the receptor. If the molecules are similar, this essentially reduces the search space to a rotational search (to a first approximation). Hence, the default distance range and angular samples are set to much smaller values than are used in a typical docking correlation search. Similarly, good global overlaps can be found using much lower-order correlations than needed for docking. Therefore, its usually sensible to leave all the superposition search parameters at their default values. Nonetheless, the defaults generally give a search which significantly over-samples the search space, and only one or two distinct superpositions are likely to remain after clustering. By default, superpositions are calculated using only the van der Waals density representation of each molecule. However, this can be changed with the Search Mode selector to match shapes using both the interior (van der Waals) and exterior (surface skin) density functions. This doubles the computational cost, but it can be useful when matching a small molecular fragment onto a surface patch of a larger molecule, because the skin-matching component ensures surface matches are favoured over trivial inclusion matches of the fragment within the body of the larger molecule. The shape matching algorithm re-uses much of the docking code, and the Matching Control panel works in almost exactly the same way as for docking (see section Docking Examples). One noticeable difference, however, is that similarity scores are calculated using a Carbo-like overlap score. This is essentially a normalised overlap volume, scaled onto [-1000,0] for compatibility with the existing clustering, ranking, and summary output code used by the docking module. In other words, Hex always thinks “negative is good.” http://hex.loria.fr/
  19. 19. -steps description and importance 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 4.Results
  20. 20. 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 4.Results -IL_2: fig1(sinix), fig 2(dex)
  21. 21. 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 4.Results -MLT: fig5,2,6,4 (in ordine orario)
  22. 22. 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014 4.Results -LPS: fig 7,3,6,4 (in ordine orario)
  23. 23. 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014
  24. 24. 8th International Conference on APPLIED MATHEMATICS, SIMULATION, MODELLING. Florence, 2014
  25. 25. 5. Conclusions -internal controls -this preliminary study has allowed to observe that the simultaneous presence of Melatonin, IL-2 and LPS resulted in changes in the behavior of ligands compared to position inside the natural receptors occupied in the absence of other ligands - It can therefore be concluded that as hypothesized, namely the existence of an interaction between neuroendocrine agents, immune substances and mediators of the inflammatory and / or antitumor response as LPS, has an effective confirmation at the level of computational simulation

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